Modular symbols for Q-rank one groups and Voronoi reduction

Paul E. Gunnells

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arXiv · math/9809058

Modular symbols for Q-rank one groups and Voronoi reduction

Paul E. Gunnells

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Abstract

We present an algorithm to compute the action of the Hecke operators on the top dimensional integral cohomology of certain torsion-free arithmetic subgroups of algebraic groups of Q-rank one. This generalizes the modular symbol algorithm to a setting including Bianchi groups and Hilbert modular groups. In addition, we generalize some results of Voronoi for real positive-definite quadratic forms to self-adjoint homogeneous cones of arbitrary Q-rank.

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Paul E. Gunnells. 1998-09-10. Modular symbols for Q-rank one groups and Voronoi reduction. https://arxiv.org/abs/math/9809058

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